Thursday 21 May 2026, 13:00, Mendelhaus SR12, Mathilde André (Collège de France and University of Vienna):

"Moment duality in branching particle models, application to the genealogies of multitype regulated populations". (Image: M. André)

 

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“Moment duality in branching particle models, application to the genealogies of multitype regulated populations”

Abstract:
Our work aims to provide a comprehensive recursive formula to grasp the distribution of the genealogies of any population model as a function of the contributions of the stochastic neutral fractions. It involves the semigroup of neutral fractions in a Feynman—Kac form, which also appears in the many-to-one formula of (Bansaye, 2025). The strength of our approach is that this semigroup can be defined for any model of population — for instance, individuals do not need to reproduce independently — making the formula quite general and of intrinsic value.
As a first application of our methodology, we study a broad class of frequency-dependent individual-based models on a finite type space. Under a second moment assumption, we close the induction. We prove the limiting distribution of the genealogies is given by the celebrated Kingman coalescent, which serves as baseline models for panmictic, neutral populations.
Thus, our result strides towards refining the intuition that neutral, Cannings-like genealogies can arise from complex interactions, extending beyond exchangeable and fix-sized populations.
Kingman’s coalescence rates are recovered from the contribution of the spinal immigration to a small deviation of the type-frequency process. The underlying structure only influences the effective population size, hence the genetic diversity of the population.
This is joint work with Félix Foutel-Rodier (Université Paris Cité) and Emmanuel Schertzer (Universität Wien).

12.05.2026